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Performance bounds for Nash equilibria in submodular utility systems with user groups

Journal of Control and Decision 2018年第1期5卷 1-18页

作者： Yajing Liu Edwin K.P.Chong Ali Pezeshki Department of Electrical and Computer Engineering Colorado State UniversityFort CollinsCOUSA Department of Electrical and Computer Engineering&Department of Mathematics Colorado State UniversityFort CollinsCOUSA

It is shown that for a valid non-cooperative utility system,if the social utility function is submodular,then any Nash equilibrium achieves at least 1/2 of the optimal social utility,subject to a function-dependent additive ***,if the social utility function is nondecreasing and submodular,then any Nash equilibrium achieves at least 1/(1+c)of the optimal social utility,where c is the curvature of the social utility *** this paper,we consider variations of the utility system considered by Vetta,in which users are grouped *** aim is to establish how grouping and cooperation among users affect performance *** consider two types of *** first type is from a previous paper,where each user belongs to a group of users having social ties with *** this type of utility system,each user’s strategy maximises its social group utility function,giving rise to the notion of social-aware Nash *** prove that this social utility system yields to the bounding results of Vetta for non-cooperative system,thus establishing provable performance guarantees for the social-aware Nash *** the second type of grouping we consider,the set of users is partitioned into l disjoint groups,where the users within a group cooperate to maximise their group utility function,giving rise to the notion of group Nash *** this case,each group can be viewed as a new user with vector-valued actions,and a 1/2 bound for the performance of group Nash equilibria follows from the result of *** as we show tighter bounds involving curvature can be *** defining the group curvature cki associated with group i with ki users,we show that if the social utility function is nondecreasing and submodular,then any group Nash equilibrium achieves at least 1/(1+max1≤i≤l cki)of the optimal social utility,which is tighter than that for the case without *** a special case,if each user has the same action space,then we have that any g

关键词： Group Nash equilibrium social-aware Nash equilibrium submodularity utility system

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Selecting Seeds for Competitive Influence Spread Maximization in Social Networks

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国际计算机前沿大会会议论文集 2016年第1期 153-155页

作者： Hong Wu Weiyi Liu Kun Yue Jin Li Weipeng Huang School of Information Science and Engineering Yunnan UniversityKunmingChina School of Computer Science and Engineering Qujing Normal UniversityQujingChina School of Software Yunnan UniversityKunmingChina

There exist two or more competing products in viral marketing, and the companies can exploit the social interactions of users to propagate the awareness of products. In this paper, we focus on selecting seeds for maximizing the competitive influence spread in social networks. First, we establish the possible graphs based on the propagation probability of edges, and then we use the competitive influence spread model (CISM) to model the competitive spread under the possible graph. Further, we consider the objective function of selecting k seeds of one product under the CISM when the seeds of another product have been known, which is monotone and submodular, and thus we use the CELF (cost-effective lazy forward) algorithm to accelerate the greedy algorithm that can approximate the optimal with 1 ? 1/e. Experimental results verify the feasibility and effectiveness of our method.

关键词： Social networks Competitive influence spread Possible graph submodularity CELF algorithm

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Influence Maximization for Cascade Model with Diffusion Decay in Social Networks

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国际计算机前沿大会会议论文集 2016年第1期 106-108页

作者： Zhijian Zhang Hong Wu Kun Yue Jin Li Weiyi Liu School of Information Science and Engineering Yunnan UniversityKunmingChina College of Science Kunming University of Science and TechnologyKunmingChina College of Computer Science and Engineering Qujing Normal UniversityQujingChina School of Software Yunnan UniversityKunmingChina

Maximizing the spread of influence is to select a set of seeds with specified size to maximize the spread of influence under a certain diffusion model in a social network. In the actual spread process, the activated probability of node increases with its newly increasing activated neighbors, which also decreases with time. In this paper, we focus on the problem that selects k seeds based on the cascade model with diffusion decay to maximize the spread of influence in social networks. First, we extend the independent cascade model to incorporate the diffusion decay factor, called as the cascade model with diffusion decay and abbreviated as CMDD. Then, we discuss the objective function of maximizing the spread of influence under the CMDD, which is NP-hard. We further prove the monotonicity and submodularity of this objective function. Finally, we use the greedy algorithm to approximate the optimal result with the ration of 1 ? 1/e.

关键词： Social networks Influence maximization Cascade model Diffusion decay submodularity Greedy algorithm

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